Wave propagation in inhomogeneous layered media: solution of forward and inverse problems
Wave propagation in inhomogeneous layered media: solution of forward and inverse problems
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DOI：
10.1007/s00707-004-0080-7
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发表时间：
2004-05
期刊：
影响因子：
2.7
通讯作者：
A. Chakraborty;S. Gopalakrishnan
中科院分区：
文献类型：
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作者：
A. Chakraborty;S. Gopalakrishnan
使用新的谱层单元 (SLE) 研究高频冲击载荷导致的各向异性非均匀层状介质中的波传播。该单元可以对功能梯度材料 (FGM) 进行建模，其中假设材料属性变化遵循指数函数。该元素对于描述模量和密度变化的单参数模型来说是精确的。这种新颖的元素是使用部分波技术 (PWT) 方法与线性代数方法相结合来制定的。保留了有限元 (FE) 公式的矩阵结构，这大大简化了多层结构的建模。开发的 SLE 具有精确的动态刚度矩阵，因为它使用频域中控制弹性动力学方程的精确解作为其插值函数。质量分布被精确建模，因此，该单元给出了每层的精确频率响应。因此，一个元件可能与一层完整的层一样大，这导致系统尺寸与传统有限元系统相比非常小。快速傅里叶变换（FFT）和傅里叶级数用于时间/空间域的反演。公式化的元素进一步用于研究多层介质中的应力分布。作为一个自然应用，研究了兰姆波在非均匀板中的传播并获得了时域描述。此外，还研究了谱公式在求解反问题（即力辨识和系统辨识）中的优势。约束非线性优化技术用于材料特性识别，而传递函数方法用于冲击力识别。
Wave propagation in anisotropic inhomogeneous layered media due to high frequency impact loading is studied using a new Spectral Layer Element (SLE). The element can model functionally graded materials (FGM), where the material property variation is assumed to follow an exponential function. The element is exact for a single parameter model which describes both moduli and density variation. This novel element is formulated using the method of partial wave technique (PWT) in conjunction with linear algebraic methodology. The matrix structure of finite element (FE) formulation is retained, which substantially simplifies the modeling of a multi-layered structure. The developed SLE has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation in the frequency domain as its interpolation function. The mass distribution is modeled exactly, and, as a result, the element gives the exact frequency response of each layer. Hence, one element may be as large as one complete layer which results in a system size being very small compared to conventional FE systems. The Fast-Fourier Transform (FFT) and Fourier series are used for the inversion to the time/space domain. The formulated element is further used to study the stress distribution in multi-layered media. As a natural application, Lamb wave propagation in an inhomogeneous plate is studied and the time domain description is obtained. Further, the advantage of the spectral formulation in the solution of inverse problems, namely the force identification and system identification is investigated. Constrained nonlinear optimization technique is used for the material property identification, whereas the transfer function approach is taken for the impact force identification.